Dual-closed-loop PI-controlled defect reconstruction algorithm and gain-scheduling strategy for electromagnetic tomography

Electromagnetic tomography (EMT) is a promising non-destructive evaluation technique for defect detection and characterization in metallic structures by reconstructing conductivity distributions from sensor array measurements. Owing to the ill-posed and underdetermined nature of the inverse problem, developing a reconstruction algorithm with high accuracy and robust stability is crucial for reliable defect characterization. Although Proportional-Integral (PI)-controlled iterative reconstruction methods, which provides feedback using a Dirichlet-to-Neumann (DtN) map, achieve superior performance compared to traditional algorithms, they still suffer from the semi-convergence effect. To address this limitation, this paper proposes a dual-closed-loop PI-controlled iterative reconstruction method, which augments the conventional single-loop framework with an additional inner loop. Specifically, the outer loop utilizes the DtN map to generate error feedback, while the inner loop employs a sensitivity-matrix-based forward calculation. By sharing cumulative historical voltage data from the outer loop, the inner loop acts as a dynamic regularization term and reduce the condition number of the inverse problem, thereby stabilizing the iterative trajectory and mitigating the semi-convergence effect. Numerical and Experimental results demonstrate that the proposed method simultaneously enhances iterative stability and yields higher-fidelity defect reconstructions. Furthermore, to reduce noise susceptibility, a robust gain-scheduling strategy based on the signal-to-noise ratio (SNR) is introduced. Validation under measurement data contaminated with varying levels of white noise reveals that this strategy, particularly with an exponential scheduling scheme, significantly enhances noise resilience and maintains high reconstruction fidelity even under severe noise levels.